A variable weight approach was proposed to handle the probability deficiency problem in the evidential reasoning （ER） approach. The probability deficiency problem indicated that the inadequate information in the assessment result should be less than that in the input. However, it was proved that under certain circumstances, the ER approach could not solve the probability deficiency problem. The variable weight approach was based on two assumptions： 1） the greater weight should be given to the rule with more adequate information; 2） the greater weight should be given to the rules with less disparate information. Assessment results of two notional case studies show that 1） the probability deficiency problem is solved using the proposed variable weight approach, and 2） the information with less inadequacy and more disparity is provided for the decision makers to help reach a consensus.
The technique for order performance by similarity to ideal solution （TOPSIS） is one of the major techniques in dealing with multiple criteria decision making （MCDM） problems, and the belief structure （BS） model has been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with BS model is proposed to solve group belief MCDM problems. Firstly, the group belief MCDM problem is structured as a belief decision matrix in which the judgments of each decision maker are described as BS models, and then the evidential reasoning approach is used for aggregating the multiple decision makers＇ judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. To measure the separation from ideal solutions, the concept and algorithm of belief distance measure are defined, which can be used for comparing the difference between BS models. Finally, the relative closeness and ranking index are calculated for ranking the alternatives. A numerical example is given to illustrate the proposed method.
为实时、准确地评价和跟踪武器装备体系(system of system,SoS)建设过程中的风险,对武器装备体系建设风险的风险因子进行模糊综合评价。分析武器装备体系建设风险的来源和成因,并将武器装备体系建设风险评价划分为5级层次,引入风险因子的概念,建立武器装备体系建设的风险评价模型,对武器装备体系建设风险进行5级模糊综合评价。该模型客观合理,为武器装备体系建设风险的评价提供了一种简单实用的方法。
